BP oil has many bonds trading on the New York Stock Exchange. Suppose BP\'s bond
ID: 2664313 • Letter: B
Question
BP oil has many bonds trading on the New York Stock Exchange. Suppose BP's bonds have identical coupon rates of 5.7% but that one issue matures in 1 year, one in 6 years, and the third in 14 years. Assume that a coupon payment was made yesterday.a. if the yield to maturity for all three bonds is 8%, what is the fair price of each bond?
b. suppose that the yield to maturity for all of these bonds changed instantaneously to 7%. What is the fair price of each bond now?
c. suppose that the yield to maturity for all of these bonds changed instantaneously again, this time to 11%. Now what is the fair price of each bond?
d. based on the fair prices at the various yields to maturity, is interest-rate risk the same, higher, or lower for longer versus shorter maturity bonds? Please show me how to alculate the answers.
Explanation / Answer
Let the face value of the bond be $1,000. Coupon rate is 5.7% for all the three bonds. Coupon payment = Coupon rate x Face value of the bond = 0.057 x $1,000 = $57 Number of years for Bond-1 = 1yr Number of years for Bond-2 = 6yrs Number of years for Bond-3 = 14yrs Yield to maturity is 8% for all the three bonds. But given that the coupon payment is made yesterday. This indicates that one year has already been completed in each bond's life. Now, the number of years will be reduced by one year for each bond. For Bond-1 = 0yrs For Bond-2 = 5yrs For Bond-3 = 13yrs Calculating the fair value of Bond-1 using excel sheet: Step1: Go to excel and click "inert" to insert the function. Step2: Select the "PV" function as we are finding the present value of the bond after one year. Step3: Enter the values as Rate = 8% , Nper = 0 ; PMT = -57; FV = -1000 Step4: Click "OK" to get the desired value. The value comes to "$1,000" Therefore, the fair value of the bond is $1,000 Calculating the fair value of Bond-2 using excel sheet: Step1: Go to excel and click "inert" to insert the function. Step2: Select the "PV" function as we are finding the present value of the bond after one year. Step3: Enter the values as Rate = 8% , Nper = 5 ; PMT = -57; FV = -1000 Step4: Click "OK" to get the desired value The value comes to "$908.17" Calculating the fair value of Bond-3 using excel sheet: Step1: Go to excel and click "insert" to insert the function. Step2: Select the "PV" function as we are finding the present value of the bond after one year. Step3: Enter the values as Rate = 8% , Nper = 13 ; PMT = -57; FV = -1000 Step4: Click "OK" to get the desired value The value comes to "$818.21" b) If the YTM canges from 8% to 7% then calculating the fair value of each bond: Calculating the fair value of Bond-1 using excel sheet: Step1: Go to excel and click "inert" to insert the function. Step2: Select the "PV" function as we are finding the present value of the bond after one year. Step3: Enter the values as Rate = 7% , Nper = 0 ; PMT = -57; FV = -1000 Step4: Click "OK" to get the desired value The value comes to "$1,000" Calculating the fair value of Bond-2 using excel sheet: Step1: Go to excel and click "inert" to insert the function. Step2: Select the "PV" function as we are finding the present value of the bond after one year. Step3: Enter the values as Rate = 7% , Nper = 5 ; PMT = -57; FV = -1000 Step4: Click "OK" to get the desired value The value comes to "$946.70" Calculating the fair value of Bond-3 using excel sheet: Step1: Go to excel and click "inert" to insert the function. Step2: Select the "PV" function as we are finding the present value of the bond after one year. Step3: Enter the values as Rate = 7% , Nper = 13 ; PMT = -57; FV = -1000 Step4: Click "OK" to get the desired value The value comes to "$891.35" c) Calculating the fair value of each bond when the YTM is 11% Calculating the fair value of Bond-1 using excel sheet: Step1: Go to excel and click "inert" to insert the function. Step2: Select the "PV" function as we are finding the present value of the bond after one year. Step3: Enter the values as Rate = 11% , Nper = 0 ; PMT = -57; FV = -1000 Step4: Click "OK" to get the desired value The value comes to "$1,000" Calculating the fair value of Bond-2 using excel sheet: Step1: Go to excel and click "inert" to insert the function. Step2: Select the "PV" function as we are finding the present value of the bond after one year. Step3: Enter the values as Rate = 11% , Nper = 5 ; PMT = -57; FV = -1000 Step4: Click "OK" to get the desired value The value comes to "$804.12" Calculating the fair value of Bond-3 using excel sheet: Step1: Go to excel and click "inert" to insert the function. Step2: Select the "PV" function as we are finding the present value of the bond after one year. Step3: Enter the values as Rate = 11% , Nper = 13 ; PMT = -57; FV = -1000 Step4: Click "OK" to get the desired value The value comes to "$642.26" d) The relation between bond prices and prevailing interest rates is neither simple nor linear. How much bond prices rise or fall depends on the terms of the bonds and the current yield of the bond. Interest rate risk is inversely proportional to the current yield to maturity of a bond- the higher the YTM the less the price will change for a given change in interest rates. The prices of long-term bonds changes by more than the prices of short-term bonds for the same change in interest rates. This results because the present value of the later coupon payments and the payment of principal is further into the future for long-term bonds, and thus is more affected by interest rates. The interest rate risk will be higher for bonds with long-term maturities than bonds with short-term maturities. Here bond prices are decreasing with increasing maturities for the given interest rates. With increasing YTM, the higher the change in bond prices. Therefore, the interest rate risk is same for longer vs short-term maturities.
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